the assumption being that h(t) is the height of the rock in "t" seconds, so by the time the rock hits the ground h(t) = 0, namely it has reached 0 height because, well, is on the ground :)
[tex]h(t)=36t^2 - 64\implies 0=36t^2 - 64\implies 64=36t^2\implies \cfrac{64}{36}=t^2 \\\\\\ \sqrt{\cfrac{64}{36}}=t\implies \sqrt{\cfrac{16}{9}}=t\implies \cfrac{4}{3}=t\implies 1.\overline{33}=t[/tex]
Look at the table of values. What is the vertex of the graph? How do you know?
The vertex of the given graph is (5, 0)
What is vertex:A vertex is a point on a polygon where two rays or line segments meet, and the sides or edges of the object come together. Vertex is the plural form of vertices.
A straight line that can be extended endlessly is known as a ray. An angle is created when two line segments or rays cross one another. A vertex is created by definition whenever two lines come together to produce an angle.
Thus, we can state that a vertex is formed when two line segments or rays intersect.
Here we have a graph
The equation of the graph is y = |x - 5| + 1
As we can see that two lines are intersected at a point (5, 0)
Therefore,
The vertex of the given graph is (5, 0)
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A circle has a radius of 3 inches. What is the circumference of the circle? (Use 3.14
for pi.)
Answer: look at the image for the answer and the solution
Step-by-step explanation:
Answer: 18.84
Step-by-step explanation:
because the radius is 3, the diameter is 6. And the circumference is C=pi(d).In this case, C=3.14(6), and 3.14*6=18.84
What is 36 + 45 rewritten as the product of a whole number and the sum of two whole numbers with no common factor
By using the distributive property the sum "36 + 45" can be expressed as product and sum of 2 numbers as 9 × (4 + 5) .
The Distributive Property states that a × (b + c) = a×b + a×c, where a, b, and c are any real numbers.
Using this property, we can rewrite the sum 36 + 45 as:
⇒ 36 + 45 = 9 × 4 + 9 × 5
Factoring out the common factor of 9,
we get ;
⇒ 36 + 45 = 9 × (4 + 5) ;
Therefore, the sum 36 + 45 as the product of a whole number (9) and a sum of two whole numbers (4 and 5) is 9×(4 + 5) .
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The given question is incomplete , the complete question is
What is 36+45 by using the distributive property to rewrite the sum as the product of a whole number other than 1 and a sum of two whole numbers ?
A rectangle i formed by placing two identical quare ide by ide. The area of the rectangle i 288 quared cm. What i the perimeter of one quare?
The perimeter of one square which combined with other to form a rectangle of 288 cm² is 12 cm.
The area of rectangle is given by the formula -
Area = length × width
Now we know that all the sides of square are same. Also, the identical squares have been kept side by side. So, let us represent one dimension of square with b. Thus, length of rectangle will be (b + b)
Length of rectangle = 2b
Width of rectangle will be b. Now, finding the value of b first.
288 = 2b×b
Performing multiplication
2b² = 288
b² = 288/2
Performing division
b² = 144
b = ✓144
Taking square root
b = 12 cm
The perimeter of one square = 2(length + width)
Perimeter of one square = 2 ( 12 + 12)
Perimeter = 2 × 24
Performing multiplication
Perimeter = 48 cm
Thus, perimeter of one square is 48 cm.
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Find a possible formula for the trigonometric function whose values are in the following table.
The formula possible formula for the trigonometric function whose values are in the following table is y = 6 x sin(π/2 * x) - 4.
What is a trigonometric function?Trigonometric functions are described as the periodic functions which denote the relationship between angle and sides of a right-angled triangle.
The formula for a trigonometric function is typically written as :
y = a sin (bx + c) + d
where a, b, c, and d are constants which tells us the amplitude, frequency, phase shift, and vertical shift of the function, respectively.
From the above table, the amplitude = 6,
the frequency is 2π/4 = π/2
the phase shift = 0, and
the vertical shift = -4.
Therefore, we can write the formula for the function as Y = 6 * sin(π/2 * x) - 4.
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I NEED HELP ON THIS FAST
4x+1/20x³ + 2⁹x²³-10X
Answer: [tex]5x^{2} +6x[/tex][tex]-4[/tex]
Step-by-step explanation:
Synthetic division
in a simple linear regression model we use the normal quantile plot of the residuals to evaluate if it is reasonable to assume the ___________ come from a normal distribution.
In a simple linear regression model we use the normal quantile plot of the residuals to evaluate if it is reasonable to assume the error term come from a normal distribution.
In a simple linear regression model, the normal quantile plot of the residuals is a graphical tool used to assess the normality assumption of the error term (also known as the residual). The error term represents the difference between the actual value of the dependent variable and the predicted value by the model.
Assuming that the error term follows a normal distribution is important for various reasons. Firstly, the normal distribution is a very common assumption in statistics, and many statistical methods rely on it. Secondly, a normal distribution of the error term is essential for making reliable predictions and for computing valid confidence intervals.
The normal quantile plot of the residuals compares the distribution of the residuals against a theoretical normal distribution. The plot consists of a straight line if the residuals are normally distributed. However, if the plot shows deviations from the straight line, it indicates non-normality in the residuals.
If the normality assumption is not satisfied, we need to explore the reasons for the non-normality and consider alternative methods to analyze the data, such as non-parametric methods.
Therefore, the normal quantile plot of residuals is an essential diagnostic tool in simple linear regression, as it allows us to evaluate the assumption of normality and make appropriate adjustments to the model.
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The measure of an angle is 84°. What is the measure of its complementary angle?
Answer:
6°
Step-by-step explanation:
Two angles are called complementary if the sum of their measures equals to 90°:
The complementary angle of 84° = 90° - 84°
= 6°
Answer: 6
Step-by-step explanation:
The complementary angle means the sum of two angles equal to 90. Let x be the other angle.
x + 84 = 90
x = 6
mr. tabor believes that less than 75% of the students at his school completed their math homework last night. the math teachers inspect the homework assignments from a random sample of 50 students at the school. what are the appropriate hypotheses for performing this significance test?
The null hypothesis statement is that the population is equal to the value mentioned in the claim:
[tex]H_{0} =P=75%=0.75[/tex]=[tex]\frac{75}{100}[/tex]=[tex]0.75[/tex].
[tex]H_{0} =P < 0.75[/tex]
The claim can be supported by either the null hypothesis or the alternative hypothesis. The null hypothesis states that the population proportion is the same as the value specified in the claim. If the null hypothesis is the assertion, then the alternative hypothesis statement is the antithesis of the null hypothesis.
[tex]H_0} =P < 0.75[/tex]
A hypothesis is a well-informed, logically-supported guess about the answer to a scientific question. Although it is the experiment's anticipated outcome, it does not constitute experimental proof. The information obtained may or may not be supported, depending on the information received. Simple hypotheses simply state the relationship between two independent and dependent variables. Examples: If you stay up late, you will feel fatigued the next day.
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I NEED ANSWER ASAP IM GIVING A LOT OF POINTS
Answer:
The answer is 26
Step-by-step explanation:
The system is easy16-6=10,15-5=1010+10+18=38For the missing number.16-15=1,8-2=61+6+19=26Need help with this for school
Answer:
135
Step-by-step explanation:
The max value is where the far right point of the "whisker" is.
Is y=5 and x=-1 parallel
Answer:
y=5 and x=-1 are parallel
Step-by-step explanation:
Let's do a quick review on some things:
Parallel lines are the lines that never intersect and perpendicular lines are the lines that intersect at 90°.
Lines with the same slope are parallel and if the slope of one line is the negative reciprocal of the second line, then they are perpendicular.
So, this answers to your question that it's parallel!
Hopefully this helps :)
5 1/2 ounce of mango has 17 1/2 grams of sugar and 4 ounces of pineapple has 25 grams of sugar
If 5 1/2 ounce of mango has 17 1/2 grams of sugar and 4 ounces of pineapple has 25 grams of sugar, We will be having 7 grams of sugar for one ounce of mango and 6 1/4 grams of sugar for one ounce of pineapple.
The problem states that we have 5 1/2 ounces of mango with 17 1/2 grams of sugar, and 4 ounces of pineapple with 25 grams of sugar. We are asked to determine the grams of sugar per ounce for each type of food. To determine the grams of sugar per ounce for each type of food, we can use the following calculations:
For mango: 5 1/2 ounces is equivalent to 11/2 + 1/2 = 2 ounces + 1 ounce/2, so we have 17 1/2 grams of sugar in 2 1/2 ounces of mango. To find the grams of sugar per ounce, we can divide 17 1/2 by 2 1/2, which gives us 7 grams of sugar per ounce of mango.
For pineapple: 4 ounces of pineapple has 25 grams of sugar. To find the grams of sugar per ounce, we can divide 25 by 4, which gives us 6 1/4 grams of sugar per ounce of pineapple.
Therefore, the grams of sugar per ounce for mango and pineapple are 7 and 6 1/4, respectively.
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Complete question is:
5 1/2 ounce of mango has 17 1/2 grams of sugar and 4 ounces of pineapple has 25 grams of sugar. Determine the grams of sugar for ounce for each type of food.
The following percentages were obtained over many years of observation by the U. S. Weather Bureau. All data listed are for the month of December.
Location
Long-Term Mean % of Clear Days in Dec.
Juneau, Alaska
18%
Seattle, Washington
24%
Hilo, Hawaii
36%
Las Vegas, Nevada
75%
Phoenix, Arizona
77%
In the locations listed, the month of December is a relatively stable month with respect to weather. Since weather patterns in these locations from one day to the next are more or less the same, it is reasonable to use a binomial probability model.
Let r be the number of clear days in December. Since December has 31 days, 0≤r≤31. Nm4u0IVE95dhb8ATPw0weRwYAkAAAAASUVORK5CY P(r)yEe62CYUPB7MJz5G6C+JLsVriPljwPUUJXmslZLy is the binomial probability for each of the listed locations when r=0, 1, 2, … , 31f+RvZvj8MDoTWn4AAAAASUVORK5CYII=. Include your formula setup or calculator comments to answer the following questions.
(1 pt) Find the probability that Juneau will have at most 8 clear days in December.
(1 pt) Find the probability the Hilo will have at least 14 clear days in December.
(1 pt) Find the probability that Phoenix will have 20 or more clear days in December.
(1 pt) Find the probability that Las Vegas will have no more than 18 clear days in December.
(2 pts) Find the probability that Seattle will have from 5 to 10 (including 5 and 10) clear days in December
The probability of having at most 8 clear days in Juneau, 14 or more in Hilo, 20 or more in Phoenix, 18 or less in Las Vegas, and between 5 and 10 in Seattle is 0.7608, 0.7367, 0.4672, 0.9590, and 0.5385, respectively.
1. P(r≤8) = P(r=0) + P(r=1) + P(r=2)+ P(r=3)+ P(r=4)+ P(r=5)+ P(r=6)+ P(r=7)+ P(r=8)= 0.7608
2. P(r≥14) = 1 - P(r≤13) = 1 - (P(r=0) + P(r=1) + P(r=2)+ P(r=3)+ P(r=4)+ P(r=5)+ P(r=6)+ P(r=7)+ P(r=8)+ P(r=9)+ P(r=10)+ P(r=11)+ P(r=12)+ P(r=13))= 0.7367
3. P(r≥20) = 1 - P(r≤19) = 1 - (P(r=0) + P(r=1) + P(r=2)+ P(r=3)+ P(r=4)+ P(r=5)+ P(r=6)+ P(r=7)+ P(r=8)+ P(r=9)+ P(r=10)+ P(r=11)+ P(r=12)+ P(r=13)+ P(r=14)+ P(r=15)+ P(r=16)+ P(r=17)+ P(r=18)+ P(r=19))= 0.4672
4. P(r≤18) = P(r=0) + P(r=1) + P(r=2)+ P(r=3)+ P(r=4)+ P(r=5)+ P(r=6)+ P(r=7)+ P(r=8)+ P(r=9)+ P(r=10)+ P(r=11)+ P(r=12)+ P(r=13)+ P(r=14)+ P(r=15)+ P(r=16)+ P(r=17)+ P(r=18)= 0.9590
5. P(5≤r≤10) = P(r=5) + P(r=6) + P(r=7)+ P(r=8)+ P(r=9)+ P(r=10)= 0.5385
The probability of having at most 8 clear days in Juneau, 14 or more in Hilo, 20 or more in Phoenix, 18 or less in Las Vegas, and between 5 and 10 in Seattle is 0.7608, 0.7367, 0.4672, 0.9590, and 0.5385, respectively.
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help please asasp tyyyyyyyyyyyy
Answer:
One pecan cheesecake = $9
One apple cheesecake = $20
Step-by-step explanation:
This is a system of equations problem, so we can set up these equations (Note: p = pecan cheesecake cost | a = apple cheesecake cost):
8p + 12a = 312
9p + 6a = 201
Now, we can solve the system of equations. Below is an example of using the elimination method to solve the system:
1. 8p + 12a = 312 --> -4p - 6a = -156
9p + 6a = 201 --> 9p + 6a = 201
2. 5p = 45
3. p = 9
4. 8(9) + 12a = 312
72 + 12a = 312
12a = 240
a = 20
1. We try to make one of the terms equal to the negative version of the other term to eliminate that term; here, I am eliminating "a". To do this, find a multiple of one of the equations where one of the terms is the negative version of the other term. In other words, divide/multiply the equation by a number so one of the terms in the equation is the negative version of the term in the other equation (I divided the first equation by -2 so 12a becomes -6a, the negative version of 6a in the second equation.
2. Next, add the two equations' corresponding terms
(-4p + 9p = 5p; -6a + 6a = 0; -156 + 201 = 45)
3. Simplify the equation (5p = 45; p = 45/5; p = 9)
4. Substitute the term you found back into one of the equations to find the other term.
2x+2y=4;8x-2y=-4
Solve for linear equations by ELIMINATION. Show your work.
The solution to the system of given linear equations is x = 0 and y = 2.
What is the equation?The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.
The system of equations is given in the question, as follows:
2x + 2y = 4 .....(i)
8x - 2y = -4 .....(ii)
To eliminate y, add the two equations together:
2x + 8x = 4 - 4
10x = 0
Solve for x:
x = 0
Now that we have x, we can substitute it back into one of the original equations to find y:
2x + 2y = 4
2(0) + 2y = 4
2y = 4
y = 4/2
y = 2
Thus, the solution is x = 0 and y = 2.
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Which of the following is equal to the square root of the cube root of 5?
Group of answer choices
5 to the power of one third
5 to the power of one sixth
5 to the power of two thirds
5 to the power of three halves
5 to the power of one sixth (5¹/⁶) will be equal to square root of the cube root of 5.
What is the definition of square root?
The square root of a number is a value that, when multiplied by itself, yields the original number. The square root is the opposite of squaring a number. As a result, squares and square roots are ideas that are connected.
If x is the square root of y, it is denoted as x=√y, or the same equation may be expressed as x² = y. √" is the radical symbol used to symbolise the numerical root here. When a positive number is multiplied by itself, it represents the number's square. The square root of a positive number yields the original value.
Now,
Given that square root of the cube root of 5 i.e. √∛5=?
=√5¹÷³
=5¹/²*¹/³
=5¹/⁶
hence,
5 to the power of one sixth (5¹/⁶) will be equal to square root of the cube root of 5.
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What is | −34 |?
????
Answer:
34
Step-by-step explanation:
The absolute value of a real number [tex]a[/tex] is [tex]a[/tex] when [tex]a[/tex] ≥ 0, or −[tex]a[/tex] when [tex]a[/tex] < 0. The absolute value of −34 is 34.
Hope it helps and have a great day! =D
The mean of x, y, and z is 55. If x+y=107 then what does z equal?
Answer:
The value of z is 58
Step-by-step explanation:
The mean is the average of a set of numbers. Mean = (sum of the numbers)/(the number of numbers).
We are told that the mean of x+y+z is = 55.
We can wriote this as:
55 = (x+y+z)/3
We learn that x+y = 107. So lets enter that number for x + y:
55 = (x+y+z)/3
55 = ((x+y)+z)/3
55 = ((107)+z)/3 [Substitution]
55 = (107+z)/3
165 = 107+z [Multiply both sides by 3]
z = 58 [Simplify]
CHECK:
Is the mean of x, y, and z 55?
55 = (x+y+z)/3 ?
55 = ((107)+z)/3 ? [Since we know x+y = 107]
55 = ((107)+58)/3 ? [Since z=58]
55 = (165)/3) ?
55 = 55 YES The value of z is 58
3=2x+y
4x+6=10y
Find what is x and what is y
Answer:
x=1 , y=1
Step-by-step explanation:
2x+y=3 - - (1)
4x+6=10y
=> 4x-10y=-6 - - (2)
Multiply eq (1) by 2, and we get ;
4x+2y=6 - -(3)
Now subtract eq (3) by eg (2)
4x+2y=6
-4x+10y=+6
12y=12
y=1
Sub value of y in eq (1)
2x+1=3
2x=2
x=1
What percentage of K25 is 25t
The percentage K 25 that is 25 t, can be found to be 1 % .
How to find the percentage ?The relationship between K and t is such that 1 K has 100 t.
This means that K 25 in terms of t, would be:
= 25 x 100
= 2, 500 t
The percentage of K that is 25 t is therefore :
= 25 / 2, 500
= 1 / 100
= 0. 01
= 1 %
In conclusion, when given the values K 25 and 25 t, then 25 t would be 1 % of K 25.
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a manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 420 gram setting. is there sufficient evidence at the 0.01 level that the bags are underfilled? based on a 37 bag sample, the manufacturer fails to reject the null hypothesis. what is the conclusion?
The conclusion is that the bag filling machine appears to be working correctly at this setting.
Based on the information provided, the manufacturer conducted a hypothesis test to determine if the bags are underfilled at the 420 gram setting. The null hypothesis (H0) is that the bags are not underfilled, while the alternative hypothesis (H1) is that the bags are underfilled.
Since the manufacturer failed to reject the null hypothesis at the 0.01 level of significance, this means that there is not enough evidence to support the claim that the bags are underfilled at the 420 gram setting. In other words, the bag filling machine appears to be working correctly at this setting.
It's important to note that the conclusion may change if the sample size or the level of significance is different. Additionally, other factors such as the accuracy of the measuring device used or the consistency of the banana chips themselves may also impact the results.
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Find an Angle Measure T ✓ The optimal tilt for Keenan's solar panelis between 58° and 60° to the horizontal. Has Keenan placed his solar panel at an optimal angle? SOLUTION COMMON ERROR 18 ft
Keenan has placed his solar panel at an optimal angle.
How determine if Keenan has placed his solar panel at an optimal angle?The cosine law is a mathematical relationship between the sides and angles of a triangle. The cosine law states that:
cos(C) = (a² + b² - c²) / 2ab
where a, b, and c are the lengths of the sides of the triangle and C is the measure of one of the angles. This law can be used to find unknown side lengths or angle measures in a triangle when given the other values.
Check the attached image for labelling.
The angle we are trying to calculate is labelled C.
cos (C) = (20² + 18² - 19²) / (2*20*18)
cos (C) = 363/720
C = cos⁻¹(363/720)
C = 59.72°
Since the angle obtained is between 58° and 60°. Thus, Keenan has placed his solar panel at an optimal angle.
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How do I do this problem.
Answer:
1. 11π/6
2. 43π/18
3. -π/4
4. - 43π/18
5. 23π/6
6. 25π/18
Step-by-step explanation:
A full circle has a measure of 360° in degrees and 2π radians in radians.
Since a full circle has a measure of 2π radians, then half a circle has a measure of π radians, and a quarter circle has a measure of π/2 radians.
1. 2π - π/6 = 11π/6
2. 61π/36 - π/2 = 61π/36 - 18π/36 = 43π/18
3. 5π/4 - π = π/4; -π/4
4. -36π/18 - 7π/18 = -43π/18
5. 2π + π + 5π/6 = 23π/6
6. 36π/18 - 11π/18 = 25π/18
Find the missing length the triangles are similar
Answer:
[tex]49[/tex]
Step-by-step explanation:
[tex]\frac{US}{UD}=\frac{UT}{UC} \implies US=\frac{(56)(14)}{16}=49[/tex]
refer to the previous two questions: what is the probability that only one of the two failure modes will occur over the life of the building? (answer correct to 3 decimal places) hint: start by thinking components of the event failure by only one mode (what options does that imply?)
Probability that only one of the two failure modes will occur over the life of the building is 0.11
The probability for failure of building
P (Failure) = P(C U E)
= P(C) - P(E) - P(CUE) - P(C|E)P(E)
Substitute 0.05 for P(C) 0.1 for P(E) and 0.2 for PC/E) in equation to find the probability for failure.
P(failure) = P(CUE)
= 0.05 +0.1 -0.2 x 0.1
= 0.13
Probability that only one of the two failure modes will occur over the life of the building
P(CE U EC) = P(ČE) + P(EC)
= P(C U E) - P(EC)]
= P(CUE) - P(C|C)P(E)
Substitute 0.13 for P(CUE) 0.1 for P(E) and 0.2 for P(CIE) in equation (3) to find P(CE UĒC).
P(CE U EC) - 0.13 - (0.2 x 0.1)
= 0.11
Hence,
Probability that only one of two failure modes will occur over the life of the building is 0.11.
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two cards are selected from a standard deck of 52 playing cards. the first card is not replaced before the second card is selected. find the probability of selecting a black card and then selecting a red card.
The probability of selecting a black card first and a red card second from a standard deck of 52 playing cards without replacement is 13/51.
The probability of selecting a black card on the first draw is 26/52, or 1/2, since there are 26 black cards in a standard deck of 52 playing cards.
After the first card is drawn, there are 51 cards remaining, of which 26 are red. Therefore, the probability of selecting a red card on the second draw, given that a black card was selected on the first draw, is 26/51.
To find the probability of both events happening (selecting a black card followed by a red card), we multiply the probabilities of each event:
P(black card first, red card second) = P(black card first) × P(red card second | black card first)
P(black card first, red card second) = (1/2) × (26/51)
P(black card first, red card second) = 13/51
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Melanie is raising money for a school trip by selling candy bars and bags of chips. The price of each candy bar is $1.50 and the price of each bag of chips is $1.25. Yesterday Melanie made $33.25 and sold 13 more candy bars than bags of chips. Determine the number of candy bars sold and the number of bags of chips sold.
Both the quantity of candy bars and bags of chips sold are Melanie sold five bags of chips and eighteen candy bars (5 + 13).
What does sold mean?A product that has been sold has been exchanged for cash. You'll notice a "Sold" sign appear in the front yard of the house across the street whenever new neighbours purchase it.
Is it sold or is it sold?In addition to being a noun, the verb sell has three different tenses: simple present, simple past, and past participle. I'll sell my current vehicle and purchase a new one. She is distributing water bottles at the football game. My old college textbooks were all sold on the internet yesterday.
Let x be the number of bags of chips sold, then the number of candy bars sold would be x + 13.
The total revenue from the sales of the bags of chips would be $1.25 * x and the total revenue from the sales of the candy bars would be $1.50 * (x + 13).
Since the total revenue was $33.25, we can set up an equation:
$1.25x + $1.50(x + 13) = $33.25
Expanding and simplifying the right side:
$1.25x + $1.50x + $19.50 = $33.25
Combining like terms:
$2.75x + $19.50 = $33.25
Subtracting $19.50 from both sides:
$2.75x = $33.25 - $19.50 = $13.75
Dividing both sides by $2.75:
x = $13.75 / $2.75 = 5
So Melanie sold 5 bags of chips and 5 + 13 = 18 candy bars.
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The class figured out that if the percent increase is 99% from the beginning of the year, the class will have enough money for every student to go on the field trip. How much money will the class need to raise for every student to go
Answer:
Step-by-step explanation:Class Trip Fund Calculation
The class figured out that if the percent increase is 99% from the beginning of the year, the class will have enough money for every student to go on the field trip. How much money will the class need to raise for every student to go
To calculate the amount of money that the class needs to raise, you can use the formula for calculating the amount after a percent increase:
amount = original amount + (original amount * percent increase / 100)
Let's assume that the original amount is x. After a 99% increase, the new amount will be:
x + (x * 99 / 100) = x * 199 / 100
So, to find the original amount, you can set up an equation:
x * 199 / 100 = amount needed for the field trip
And then solve for x:
x = amount needed for the field trip * 100 / 199
So, the class needs to raise an amount equal to the amount needed for the field trip * 100 / 199 to have enough money for every student to go on the field trip.
Given ƒ (z) — 5(x − 6)³ + 4, classify each statement about ƒ-¹ (z) as true or false. The point of symmetry on f-¹(x) is (4,6). The domain of f-¹(x) is (-∞,4). The graphs of f¹(x) and f(x) are reflections across the x axis. The range of f¹(x) is (-∞,∞). True False OO O
The correct classification of the statements is: False, True, False, True.
What is Function ?
Function can be defined in which it relates an input to output.
The point of symmetry on f-¹(x) is (4,6).
False. The point (4,6) is not on the graph of f-¹(x), so it cannot be the point of symmetry. We can verify that the function is not symmetric with respect to any vertical or horizontal line.
The domain of f-¹(x) is (-∞,4).
True. The cube root function is defined for all real numbers, so the expression inside the cube root must be nonnegative. Therefore, (z - 4) / 5 ≥ 0, which implies that z ≥ 4. This means that the domain of f-¹(x) is (-∞,4].
The graphs of f¹(x) and f(x) are reflections across the x-axis.
False. The graphs of f¹(x) and f(x) are not reflections across the x-axis. We can plot the functions to see that they have different shapes and are not symmetric with respect to the x-axis.
The range of f¹(x) is (-∞,∞).
True. The cube root function is defined for all real numbers, so f-¹(z) can take any real value. This means that the range of f¹(x) is (-∞,∞).
Therefore, the correct classification of the statements is: False, True, False, True.
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